BN parameter learning from small datasets based on uncertain priors

Most of the previous efforts on parameter learning of BN are made ignoring the uncertainty of knowledge. To solve this problem, a probability value is attatched to each expert statement to depicit the uncertainty of the expert knowledge. The weight of each combination of these expert knowlegde is computed and the parameters under this combination are estimated following convex optimization framework. Each of these convex optimization problems is then decomposed into a series of sub problems which can be solved in parallel. Finally, a weighted average is adopted to trade off the estimated result obtained by different combinations. The validity of the proposed approach is verified using a situation assessment model.